## Research

Currently, our main research focuses on the study of

"rough sets". Our approach consists on using Category Theory to implement rough sets.Within the abstract framework provided by Category Theory, we study some structures aiming a solid background for the developing of a general framework for unification. In particular we work with sets of terms. Monads, in these context, represent a foundamental point in our research. We have studied how monads can be used to generalise and interpret rough situations. In particular we have shown how the partially ordered monad contains enough structure to provide rough operations. In order to define rough approximations, we use the natural transformations in the monad. The specific properties of partially ordered monads guarantee the equivalence to the classical rough situation and, at the same time, provide an enviroment for the study of a more general situation. In this sense, the study of rough sets from a categorical point of view, simplifies the definitions and opens the doors to new conexions.

Research Groups

**Algebra and Logic in Computer Science****GIMAC (Mathematics Applied to Computing)**

Publications

Thesis:

- María Ángeles Galán García

Categorical Unification

PhD Thesis

I.S.B.N: 91-7305-642-1 I.S.S.N: 0348-0542

http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-245

Editorial: University Library, Umea University (Sweden) Year: 2004 - María Ángeles Galán García

Generalised Terms

Licenciate Thesis

I.S.S.N: 0348-0542 Year: 2001

Book Chapters:

- P. Eklund, M.A. Galán, J. Karlsson

Categorical Innovations for Rough Sets. Studies in Computational Intelligence, Springer-Verlag Series. Acepted, To appear 2008.

Journal papers, ENTCS and LNAI:

- P. Eklund, M.A. Galán

*Partially Ordered Monads and Rough Sets. Transactions of Rough Sets, Lecture*

Notes in Computer Science, Springer-Verlag. LNCS 5084, pp. 53-74, 2008. - P. Eklund, M.A. Galán

*Partially ordered monads for monadic topologies, rough sets and Kleene algebras. Electronic Notes in Theoretical Computer Science. To appear 2008.* - P. Eklund, M.A. Galán, J. Medina, M. Ojeda-Aciego, A. Valverde

*Powersets of terms and composite monads*. Fuzzy Sets and Systems, 2007. Volume

158, Issue 23, Pages 2552-2574 (1 December 2007). - P. Eklund, M.A. Galán

*The Rough Powerset Monad*. Journal of Multiple-Valued Logic and Soft Computing, 2007. Volume 13, Number 4-6, pp. 321-334, 2007. - P. Eklund, M.A. Galán

*On Logic with Fuzzy and Rough Powerset Monads.*Proc. Rough Sets and Intelligent Systems

Paradigms (RSEISP) 2007, Warsaw, Poland. Edited by Kryszkiewicz, M. ; Peters, J.F. ; Rybinski, H. and Skowron, A. Lecture Notes in Artificial Intelligence 4585, pp. 391-399, Springer-Verlag.

- P. Eklund, M.A. Galán

*Monads can be rough*. S. Greco et al. (Eds.), Proc. Fifth Internat. Conf. Rough Sets

and Current Trends in Computing (RSCTC 2006), Lecture Notes in Artificial Intelligence

4259 (2006), 77-84.

- P. Eklund, M.A. Galán, J. Medina, M. Ojeda-Aciego, A. Valverde

*Similarities between powersets of terms*. Fuzzy Sets and Systems, 2004. Volume

144, Issue 1, Pages 213-225 (16 May 2004) Possibilistic Logic and Related Issues Edited by:

L. Godo and S. Sandri.

- P. Eklund, M.A. Galán, J. Medina, M. Ojeda-Aciego, A. Valverde

*Set functors, L-fuzzy set categories and generalized terms*. Computers and Mathematics

with Applications 43, pp. 693–705, 2002.

- P. Eklund, M.A. Galán, J. Medina, M. Ojeda Aciego, A. Valverde

*A categorical approach to unification of generalised terms.*Electronic Notes in Theoretical Computer Science. Volumen 66 (5), 11 pág. 2002.

- P. Eklund, M.A. Galán, J. Medina, M. Ojeda Aciego, A. Valverde

*A graphical approach to monad compositions*. Electronic Notes in Theoretical Computer Science. Volumen 40, 2001.

Conference papers (refereed):

- P. Eklund, M.A. Galán, J. Kortelainen

*On fuzzy successors. 12th Information Processing and Management of*

Uncertainty in Knowledge- Based Systems Conference (IPMU 2008), pp.124-128. Málaga, Spain 2008. - P. Eklund, M.A. Galán, J. Karlsson

*Rough monadic interpretations of pharmacologic information*. Proceedings of the 15th International Workshops on Conceptual Structures, ICCS 2007, pp. 108-113. Sheffield, UK.

- P. Eklund, M.A. Galán

*The Rough Powerset Monad*. Proceedings of the 37th International Symposium on Multiple Valued Logics, ISMVL-2007. Oslo (Noruega), 2007. - P. Eklund, M.A. Galán, W. Gähler

*Partially ordered monads for monadic topologies, Kleene algebras and rough sets.*Proceedings of the Fourth Irish Conference on the Mathematical Foundations of Computer Science and Information Technology, MFCSIT 2006, pp.349-352. Cork, Ireland. - P. Eklund, M.A. Galán, W. Gähler, J. Medina, M. Ojeda Aciego, A. Valverde

*A note on partially ordered generalized terms*. Proc. of Fourth Conference of the European Society for Fuzzy Logic and Technology and Rencontres Francophones sur la Logique Floue et ses applications (Joint EUSFLAT-LFA 2005), pp. 793-796. Barcelona 2005, Spain.

- P. Eklund, M.A. Galán, J. Medina, M. Ojeda Aciego, A. Valverde

*A framework for unification using powersets of terms*. 9th Information Processing and Management of Uncertainty in Knowledge-Based Systems Conference (IPMU 2002), pp. 1095–1094. Annecy (Francia), 2002.

- P. Eklund, M.A. Galán, J. Medina, M. Ojeda Aciego, A. Valverde

*Set functors and L-fuzzy set categories: towards a fuzzy programming paradigm.*Second International ICSC Symposium on Fuzzy Logic and Applications, pp. 658–664. Bangor (Reino Unido), 2001.

- P. Eklund, M.A. Galán, J. Medina, M. Ojeda Aciego, A. Valverde

*Composing submonads*. International Symposium on Multiple Valued Logics, pp. 367–372. Warsaw

(Polonia), 2001.

- P. Eklund, M.A. Galán, J. Medina, Manuel Ojeda Aciego, A. Valverde

*Generalized terms and composition of monads*. 10th Spanish Congress on Fuzzy Logic and Technologies (ESTYLF 2000), pp. 155-160. Sevilla, 2000.

- P. Eklund, M.A. Galán, Manuel Ojeda Aciego, A. Valverde

*Set functors and generalised terms*. 8th Information Processing and Management of Uncertainty in Knowledge-Based Systems Conference (IPMU 2000), pp. 1595-1599.